A Generalizable Graph Transformer Model for the Eigenspectrum of Superconducting Circuits

While superconducting quantum circuits represent one of the most promising approaches to fault tolerant quantum computing, numerical simulation of such systems is limited by the exponential scaling of the Hilbert space dimension. In this work, we build off of the SQcircuit numerical package to explore the use of graph neural networks with transformer architectures as a means of rapidly inferring the eigenspectrum of a superconducting quantum circuit. Models trained on nine circuit topologies exhibit 96\%+ weighted accuracy, with inference more than four orders of magnitude faster than diagonalization. Across a variety of out-of-distribution shifts over multiple seeds, we also show that message passing proves essential for inductive bias towards unseen topologies. We also provide evidence that global self-attention and Sobolev gradient loss terms improve zero-shot performance and model stability.